Resource-Efficient Discrete Fourier Transform via the Goertzel Algorithm for Continuous Wave Detection with FPGAs
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Date
2025-05
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The Ohio State University
Abstract
In many digital signal processing (DSP) applications, the Discrete Fourier Transform (DFT) is used as a method of breaking down a signal into its corresponding frequency components. It is a conversion of a discretized finite-duration signal from the time domain into the frequency domain, producing a discrete power spectrum. A field-programmable gate array (FPGA) is an integrated circuit (IC) with reconfigurable internal logic. Because of their capabilities for parallel mathematical operations, FPGAs lend themselves to complex signal processing applications, and can often be a substitute for otherwise expensive, specialized hardware. Standard fast Fourier transform (FFT) algorithms often require more FPGA resources than is desirable. The Goertzel algorithm presents itself as an alternative, allowing the DFT to be cast as a type of digital filter which determines the Fourier coefficient of a single frequency. In some applications this “single-tone” DFT may not be entirely useful; however, the system benefits greatly from the filter’s minimized usage of logic elements such as registers, multipliers, and accumulators; in other words, the filter’s “hardware footprint” is far smaller than commonly used FFT alternatives, elevating it as a candidate for integration with the CoRaLS experiment.
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Keywords
Goertzel Algorithm, Discrete Fourier Transform (DFT), Field-Programmable Gate Array (FPGA), Analog-to-Digital-Converter (ADC), Digital Signal Processing (DSP), Digital Filter